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Find the greatest integer value of b for which the expression (9x^3+4x^2+11x+7)/(x^2+bx+68) has a domain of all real numbers.

 Jun 30, 2022
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The discriminant of   x^2 + bx + 68   must be < 0

 

So

 

b^2 - 4(1) (68)  < 0

 

b^2  - 272 < 0

 

b^2  < 272

 

This will be true when      -sqrt (272) < x < sqrt (272)

 

Greatest integer value for b =   floor[ sqrt (272) ] =    16

 

 

cool cool cool

 Jun 30, 2022

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